Hence construct explicitly a decreasing differentiable function g(x) such that lim g(x) = 0 lim g'(x) = 0. #448 x4+x but

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Give an example of a decreasing continuous function on [0, 1], differentiable
on (0, 1) with
f(0) = 1,
f(1) = 0,
f(0) = f(1) = 0.
Hence construct explicitly a decreasing differentiable function g(x) such that
lim g'(x) = 0.
x→+∞
lim g(x) = 0
x→+∞
but
Transcribed Image Text:Give an example of a decreasing continuous function on [0, 1], differentiable on (0, 1) with f(0) = 1, f(1) = 0, f(0) = f(1) = 0. Hence construct explicitly a decreasing differentiable function g(x) such that lim g'(x) = 0. x→+∞ lim g(x) = 0 x→+∞ but
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